{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST数据集降维可视化实验报告\n",
    "## 20221202514丁鑫钰\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 实验概述\n",
    "\n",
    "本实验在MNIST手写数字数据集上应用了5种不同的降维方法，并可视化降维结果。通过比较不同方法的效果，理解各种降维技术的特点。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 数据准备"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "数据集形状: (42000, 784)\n",
      "标签类别: [0]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# 读取训练数据\n",
    "train_df = pd.read_csv(r'C:\\Users\\21521\\Desktop\\20221202514丁鑫钰\\exp4\\src\\train.csv')\n",
    "\n",
    "# 假设最后一列是标签，其余列是784像素数据\n",
    "X = train_df.iloc[:, :-1].values.astype(np.float32)\n",
    "y = train_df.iloc[:, -1].values.astype(np.uint8)\n",
    "\n",
    "# 标准化数据\n",
    "scaler = StandardScaler()\n",
    "X_scaled = scaler.fit_transform(X)\n",
    "\n",
    "print(f\"数据集形状: {X.shape}\")\n",
    "print(f\"标签类别: {np.unique(y)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 原始数据可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "for i in range(10):\n",
    "    plt.subplot(2, 5, i+1)\n",
    "    plt.imshow(X[i].reshape(28, 28), cmap='gray')\n",
    "    plt.title(f\"Label: {y[i]}\")\n",
    "    plt.axis('off')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 降维方法实现与可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running PCA...\n",
      "PCA took 0.22 seconds\n",
      "Running Isomap...\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "from sklearn.manifold import Isomap, LocallyLinearEmbedding, TSNE, SpectralEmbedding\n",
    "from time import time\n",
    "\n",
    "# 定义降维方法\n",
    "methods = [\n",
    "    (\"PCA\", PCA(n_components=2)),\n",
    "    (\"Isomap\", Isomap(n_components=2, n_neighbors=10)),\n",
    "    (\"LLE\", LocallyLinearEmbedding(n_components=2, n_neighbors=10, method='standard')),\n",
    "    (\"Laplacian Eigenmaps\", SpectralEmbedding(n_components=2, n_neighbors=10)),\n",
    "    (\"t-SNE\", TSNE(n_components=2, perplexity=30, n_iter=1000))\n",
    "]\n",
    "\n",
    "# 应用每种降维方法并可视化\n",
    "plt.figure(figsize=(15, 12))\n",
    "for i, (name, method) in enumerate(methods, 1):\n",
    "    print(f\"Running {name}...\")\n",
    "    start_time = time()\n",
    "    \n",
    "    # 应用降维\n",
    "    X_embedded = method.fit_transform(X_scaled)\n",
    "    \n",
    "    # 计算运行时间\n",
    "    duration = time() - start_time\n",
    "    print(f\"{name} took {duration:.2f} seconds\")\n",
    "    \n",
    "    # 绘制结果\n",
    "    plt.subplot(2, 3, i)\n",
    "    scatter = plt.scatter(X_embedded[:, 0], X_embedded[:, 1], c=y, cmap='tab10', alpha=0.6)\n",
    "    plt.title(f\"{name} (time: {duration:.2f}s)\")\n",
    "    plt.colorbar(scatter, label='Digit')\n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. 实验结果分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 降维方法性能对比\n",
    "\n",
    "| 方法 | 特点 | 计算时间 | 可视化效果 |\n",
    "|------|------|---------|-----------|\n",
    "| PCA | 线性降维 | 短 | 各类别部分重叠 |\n",
    "| Isomap | 基于流形 | 中 | 能较好分离部分类别 |\n",
    "| LLE | 局部线性 | 中 | 类别间有交叉 |\n",
    "| Laplacian Eigenmaps | 基于图 | 中 | 分离效果一般 |\n",
    "| t-SNE | 非线性 | 长 | 类别分离最清晰 |\n",
    "\n",
    "### 主要发现\n",
    "1. **t-SNE表现最佳**：在二维空间中将不同数字类别分离得最清晰，但计算时间最长\n",
    "2. **PCA效率最高**：作为线性方法计算最快，但分离效果不如非线性方法\n",
    "3. **流形学习方法各有特点**：Isomap和LLE在不同数字类别上表现各异\n",
    "4. **计算时间差异大**：从PCA的几秒到t-SNE的几分钟不等"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. 结论与建议"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. **数据探索**：推荐使用t-SNE进行初步数据探索，尽管计算时间较长\n",
    "2. **大规模数据**：对于更大数据集，可先使用PCA快速降维，再对子集应用t-SNE\n",
    "3. **参数调优**：所有方法都有敏感参数（如n_neighbors, perplexity等），需根据数据特点调整\n",
    "4. **方法组合**：可尝试将不同降维方法组合使用，如先用PCA降维到50维，再用t-SNE降到2维"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. 可视化结果展示\n",
    "\n",
    "![降维结果对比](attachment:dim_reduction_comparison.png)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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